Here's one of the main differences:
Sometimes data engineers do DAD, sometimes data scientists do ETL, but it's rather rare, and when they do it, it's purely internal (the data engineer doing a bit of statistical analysis to optimize some database processes, the data scientist doing a bit of database management to manage a small, local, private database of summarized info (not used in production mode usually, though there are exceptions).
Let me explain what DAD means:
Discover: Find, identify the sources of good data, and the metrics. Sometimes request the data to be created (work with data engineers, business analysts).
Access: Access the data. Sometines via an API, a web crawler, an Internet download, a database access or sometimes in-memory within a database.
Distill: Extract essence from data, the stuff that leads to decisions, increased ROI and actions (such as determining optimum bid prices in an automated bidding system). Involves